1 Introduction

Hypertension or elevated blood pressure (BP) is a critical medical condition that significantly enhances the risks of developing brain, kidney, heart, and other diseases [1, 2]. Continuous BP measurement and monitoring the variations in BP are essential for regulating high BP and early intervention in hypertension and other cardiovascular disorders [3]. Sphygmomanometery and oscillometry are frequently used for monitoring BP at domicile and mobile [4, 5]. Inflatable cuffs are used to measure non-invasive BP, which can be uncomfortable, especially for hypertensive patients who need regular readings. Since stress or anxiety can arise in patients using the cuff-based approach, the measured BP results can be influenced by this [6]. As a result, cuff-based methods have been proven to be a hindrance to the widespread use of BP monitoring. Therefore, non-invasive and continuous methods for BP estimation are highly required for alleviating hypertension.

Recent advances in sensor technology have made it possible to monitor physiological parameters unobtrusively anywhere, anytime [7,8,9]. In this regard, photoplethysmogram (PPG) signal is crucial for the assessment of vital health-related factors without a reference signal and clinical condition [10]. PPG is a simple, low cost optical technique having the ability to detect the variations in blood volume in the microvascular bed of tissue with each cardiac cycle [9]. A typical two-pulse PPG signal with its characteristic points is depicted in Fig. 1. PPG’s simplicity, portability, and low cost enable its integration into mobile and wearable devices, giving an alternative for ubiquitous monitoring [7, 11]. However, despite these benefits, PPG technology’s susceptible nature towards noise and motion artifacts caused by moving fingers or hands extends the space between the sensor and the user’s skin and alters the signal quality [12]. This hinders the robust assessment of physiological parameters, making them impracticable for clinical applications [13].

Fig. 1
figure 1

A typical two-pulse PPG signal with its characteristic points. Here, x and y portrait the amplitudes of systolic and diastolic peaks, respectively, and \(\Delta T\) is the time period between these two points. \(A_1/A_2\) is the ratio of inflection

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In recent years, machine learning approaches have been used to attain excellent outcomes for continuous BP measurement using PPG signals. Recent researches have established the relation between the PPG signal and BP values [14,15,16,17,18]. Non-invasive BP estimation from PPG signals can be done by analyzing two PPG pulse waves or a PPG pulse wave along with an electrocardiogram wave [19]. Researches have been continued to explore methods of estimating BP using features of the PPG signal only. X. Teng and Y. Zhang in [20] utilized only the PPG signals to measure BP for the first time. N. Hasanzadeh et al. in [14] proposed a BP estimation method using PPG signal and its morphological features. M. H. Chowdhury et al. in [15] used 107 demographic features for estimating BP from the PPG signal. In addition, ReliefF feature selection (FS) method was applied to select optimal feature set. P. Li et al. in [21] developed a feed-forward neural network to estimate the BP using PPG features extracted by semi-classical signal analysis tools. Recently, deep neural networks have become the most widely used method because of their accurate results and cost-effective alternative to conventional machine learning methods [17, 21, 22]. A few BP estimation techniques from PPG signals are described in the literature, but most of them used only traditional machine learning methods and conventional feature selection techniques [23]. However, there were no specific feature selection algorithms to obtain the optimal feature set. Therefore, this paper aims to develop the deep learning approach along with an ensemble feature selection technique for the estimation of BP.

This paper proposes a cuff-less and continuous BP monitoring technique based on the characteristic features of the PPG signal and deep neural network. PPG signals are acquired from 219 subjects and checked the signal quality. Various preprocessing algorithms are applied to reduce noise and motion artifacts. After denoising, a total of 46 time and frequency domain features are extracted from the PPG signal, as well as its derivatives and first Fourier Transformed of PPG signal. An ensemble feature selection algorithm is applied to select the optimal feature set based on the voting of four FS techniques. Finally, DNN models are developed to estimate the SBP and DBP values. The major contributions of this paper are summarized as follows:

  • Preprocessing the PPG signal, including the filtering, removing baseline wander (BW), and PPG wave normalization.

  • Developing a peak detection algorithm and extracting a single PPG wave cycle having the highest positive systolic peak from the overall PPG waveform using it.

  • Extracting the various domain features from preprocessed selected PPG cycle and its derivatives.

  • Selecting the optimal features set through ensemble feature selection technique.

  • Constructing DNN-based models with 10-fold cross-validation to estimate the SBP and DBP.

The sequence of the remaining sections of the paper is as follows: Section 2 describes the background details and motivation of the research. Section 3 describes the proposed methodology for cuff-less blood pressure estimation. Section 4 demonstrates feature selection results, the performance of proposed algorithm and its comparison with health standards and other works. Finally, Section 5 terminates the paper with future directions.

2 Background and related works

This section describes the recent studies that rely on only PPG signals to estimate BP. In the recent decade, many approaches for measuring cuff-less BP have been proposed as alternatives to traditional methods. M. Kachuee et al. [8] extracted whole-based and physiological features and used the adaptive boosting algorithm (AdaBoost) to achieve a higher accuracy. One of the limitations of the proposed method is that the accuracy decreases due to lack of calibration. A. Gaurav et al. [24] extracted 8 PPG signal magnitude and temporal features and 19 more features from PPG’s second derivative, called the acceleration plethysmogram waveform. These features were used to train and validate three artificial neural network (ANN) regression models for each DBP and SBP. However, the results for BP estimation were unsatisfactory because age and gender were not used as features. In another study, Y. Zhang and Z. Feng [16] applied a support vector machine (SVM) to predict BP, compared it with linear regression and ANN, and achieved better accuracy. Features were extracted from more than 7000 heartbeats and 9 parameters. However, the results for the estimation of BP were not good enough; mean error is \(11.64 \pm 8.20\) mmHg for SBP and \(7.617 \pm 6.78\) mmHg for DBP. S. S. Mousavi et al. [25] extracted whole-based features proposed by M. Kachuee et al. [8] and time or frequency domain features. N. Hasanzadeh et al. [14] presented a new algorithm for the robust detection of PPG key points and extracted some morphological key features. Therefore, the proposed method achieved a good correlation between the estimated BP and its actual value. The main drawback of their algorithm is that the accuracy of the algorithm decreases if the percentage of actual class members decreases.

Table 1 Brief summary of the related works
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A. Chakraborty et al. [7] introduced two distinct approaches for the estimation of SBP, MAP, and DBP, respectively. The first method used the Two-Pulse Synthesis (TPS) model based on the initialization method, while the second method used a learning based non-parametric regression technique for the measurement of BP. M. Panwar et al. [17] developed a model named PP-Net with a customized Long-term Recurrent Convolutional Network (LRCN), utilizing the convolutional neural network and long short-term memory for estimating the physiological parameters using a single channel PPG signal.

For each PPG signal, M. H. Chowdhury et al. [15] retrieved 107 features, including 65 time-domain, 16 frequency-domain, 10 statistical features along with 6 demographic data. The ReliefF feature selection method with gaussian process regression (GPR) showed promising results for introducing an accurate cuffless BP monitoring system. P. Li et al. [21] used the semi-classical signal analysis (SCSA) method to extract features from the PPG signal and compared the output results, and SVM with SCSA produced the overall highest accurate estimates among decision tree, multiple linear regression, and SVM. In addition, a single feed-forward neural network (FFNN) was utilized for BP estimation with PPG features, which are extracted by SCSA. S. Maqsood et al. [22] evaluated the performance of machine learning approaches, including traditional machine learning and deep learning. The experiment, which used the PPG-BP dataset and MIMIC-II database, demonstrated that time-domain characteristics performed better when deep learning methods were used. For SBP and DBP estimation, Gated Recurrent Units (GRU) and Bi-Directional Long Short-Term Memory (Bi-LSTM) provided the best results using time-domain features, respectively.

Table 1 represents several existing methods to estimate the blood pressure. Motivated by the advantages of PPG technology and shortcomings of the existing studies, we focus on developing an efficient deep learning framework with feature engineering for a better robust system. In addition, an ensemble feature selection technique is proposed to obtain the optimal features based on major voting scores.

3 Methodology

The overall architecture of the proposed cuff-less BP estimation algorithm is shown in Fig. 2. The main steps of the proposed method are as follows: (i) extracting the PPG signal as the primary input and checking the signal quality, (ii) applying the preprocessing algorithms on PPG signal for denoising and correcting the BW, (iii) extracting the characteristic wave features from preprocessed PPG signals, (iv) employing an ensemble feature selection strategy for selecting optimal feature set, (v) constructing DNN-based models with 10-fold cross-validation, and (vi) finally evaluating estimation accuracy of the models for SBP and DBP.

Fig. 2
figure 2

Block diagram of the proposed blood pressure estimation algorithm

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3.1 Basic principles

The fundamental principle of estimating BP with pulse transit time (PTT) is based on evaluating the velocity of pulse wave (PW) from its traveling time between two specific sections of the traveling path. The overall concept of pulse wave propagation through an artery can be modeled by propagating a pressure wave interior an elastic cylindrical tube with mechanical properties similar to arterial walls to correlate wall elasticity to PTT. The elasticity of an artery and the velocity of the pulse waves propagating through it are profoundly related. At each ventricular contraction, blood is ejected from the lower chambers of the heart to the arterial system by affecting the velocity of the blood, resulting in a pressure wave that travels along the elastic arteries [26]. It has been shown that elastic modulus (E) of the tube is related to the fluid pressure (P) for central arteries in an exponential manner as

$$\begin{aligned} E = E_O.e^{\alpha .(P - P_O)} \end{aligned}$$
(1)

where \(E_O\) is the elastic modulus at zero fluid pressure \(P_O\) and \(\alpha \) is a correction factor.

The elasticity of the tube is described as far as Compliance (C), which is defined as the rate of change in cross-sectional area \((A_m)\) of the tube with respect to pressure. C is determined by solving the conservation of mass and momentum equations, and it can be expressed as the function of P as in [8, 27]:

$$\begin{aligned} {C(P)} = \frac{A_m}{\pi P_1 [1 + (\frac{P-P_0}{P_1})^2]} \end{aligned}$$
(2)

where \(A_m\), \(P_0\), and \(P_1\) vary from subject to subject.

Pressure wave propagating through a cylindrical shape elastic tube (see Chapter 3 of [28] for derivation) can be expressed mathematically as

$$\begin{aligned} {P(x,t)} = f(x \pm t/\sqrt{LC(P)}) \end{aligned}$$
(3)

where x and t indicate space and time, respectively. According to this wave propagation equation, the velocity of pulse traveling along an artery, PWV, is \(1/\sqrt{LC(P)}\), where \(L = \rho /A\), in which \(\rho \) is the density of blood. Hence, PTT, the time interim for navigating the pulse wave through a tube of length k, is expressed as

$$\begin{aligned} {PTT} = K\sqrt{LC(P)} \end{aligned}$$
(4)

Substituting the value of C(P) and L, Eq. 4 can be rewritten as

$$\begin{aligned} {PTT} = K\sqrt{ \frac{\rho A_m}{\pi AP_1 [1 + (\frac{P-P_0}{P_1})^2]}} \end{aligned}$$
(5)

where P is mean BP. Thus, it is elucidated from Eq. 5 that there exists an inverse relationship between PTT and BP. By Eq. 5, we can only estimate the mean BP with PTT based on arterial wave propagation model. However, DBP and SBP can also be estimated by new proposing indicator, PPG intensity ratio (PIR) [29] in terms of PTT. By solving the \(M-K\) equation, we find that pulse pressure, PP, is inversely proportional to \(PTT^2\) [30]. PP can be expressed in terms of PTT as

$$\begin{aligned} {PP} = PP_0 (\frac{PTT_0}{PTT})^2 \end{aligned}$$
(6)

where \(PP_0\) and \(PTT_0\) are initial calibrated values of PP and PTT, respectively. According to the two-element Windkessel model, as shown in [31], DBP is inversely proportional to the first power of PIR:

$$\begin{aligned} {DBP} \propto \frac{1}{PIR} \end{aligned}$$
(7)
Table 2 Statistical patient details
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Fig. 3
figure 3

Comparison of the PPG waveforms that are appropriate (fit) and inappropriate (unfit) in this study. a Appropriate PPG signal. b Inappropriate PPG signal

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Fig. 4
figure 4

PPG signal a before and b after normalization

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This indicates that DBP can easily be estimated from Eq. 7 with the aid of initially calibrated values of DBP and PIR are \({DBP}_O\) and \(PIR_O\), respectively.

$$\begin{aligned} {DBP} = DBP_0 \frac{PIR_0}{PIR} \end{aligned}$$
(8)

Since PP is the difference between SBP and DBP [32], so SBP can be derived from Eqs. 6 and 8 as

$$\begin{aligned} {SBP} = DBP_0 \frac{PIR_0}{PIR} + PP_0 (\frac{PTT_0}{PTT})^2 \end{aligned}$$
(9)

3.2 Data description

In this paper, the online PPG-BP database was used as a source for the PPG signals [33]. Liang et al. [34] analyzed and evaluated the quality of these PPG signals. The authors developed a custom portable hardware system that consisted of a PPG sensor probe, a MSP430FG4618 microcontroller, and a specialized Android application for data management. The PPG sensor was equipped with dual LEDs with 660 nm (red light) and 905 nm (infrared) wavelengths, offering a high sampling rate of 1 kHz, a 12-bit analog-to-digital converter (ADC), and a bandpass hardware filter with a frequency range of 0.5 to 12 Hz. The MSP430FG4618 microcontroller was embedded on the probe to manage the ADC, collect data, and transmit it via Bluetooth to the app. Arterial blood pressure measurements were obtained using the Omron HEM-7201 upper arm monitor. The left index finger was used to collect fingertip PPG signal, and Omron HEM-720 was used for the collection of reference BP. The assessment of BP was carried out by a nurse within the hospital setting. Three PPG segments were collected from each subject during the BP recording. Therefore, the dataset consists of 657 recorded PPG signals from 219 subjects. The sampling rate of PPG signals was 1 kHz, and the duration of each signal was 2.1 s. Table 2 demonstrates the description of the basic physiological information and a concise statistical summary.

Several PPG signals in the dataset were noisy and unsuitable for feature extraction. The quality assurance process was applied to eliminate the unacceptable quality of the PPG signal by using the skewness quality index (SQI) [34]. The final dataset consists of 218 recorded signals associated with 125 unique subjects. Each recorded signal has its own unique ID. The unique ID is used in this study in order to prevent overlapping the subjects of the training set with the test set in DNN-based model. To evaluate the skewness quality index, the PPG signal was divided into two categories: appropriate and inappropriate, shown in Fig. 3. The fit waveforms have apparent systolic and diastolic features with dicrotic notches, and the unfit waveforms do not have dicrotic notch and other informative features.

3.3 Preprocessing signals

To get quality waveforms, various pre-processing approaches were used to eliminate the noise in the PPG signals [33]. After preprocessing, approximately 125 subjects were included for evaluation.

3.3.1 Normalization

Data normalization reduces data analysis complication. Through PPG signal normalization, the information within a database can be formatted in such a way that it can be visualized and analyzed. In this study, the PPG signal was normalized using the z-score method to get amplitude-limited data.

$$\begin{aligned} {PPG}_n = \frac{{PPG}_O - \mu ({PPG}_O)}{\sigma ({PPG}_O)} \end{aligned}$$
(10)

where \({PPG}_O\) represents the original PPG signal and \({PPG}_n\) indicates normalized version of \({PPG}_O\). \(\mu \) and \(\sigma \) denote the mean and standard deviation of the original PPG signal, respectively. Figure 4 shows the sample PPG signal before and after normalization.

3.3.2 Signal filtration

The raw PPG signal of the database [33] contains so many noise components. The primary purpose of filtering a signal is to smooth out and reduce high-frequency noise associated with measurement, such as power line interference, motion artifact, low amplitude of the PPG signal, etc. [35]. Firstly, filtering techniques were tested, such as \(7^{\text {\tiny th}}\) order low pass Butterworth filter [36], 9th order low pass cheby 1 filter, removing coverage FIR filter, Discrete Wavelet Transform (DWT) [37], and Fast Fourier Transform (FFT) [38].

Finally, low pass Butterworth filter is selected because, compared to the other methods, it was analyzed that low pass Butterworth filter provides several merits such as a better phase response, better visualization of systolic and diastolic peak, and more efficiency in terms of maximum noise reduction. Figure 5 shows that the \(7^{\text {\tiny th}}\) order low pass Butterworth filter with a cut-off frequency of 15 Hz produced the best noiseless signal which was designed in MATLAB.

3.3.3 Baseline correction

BW is a low-frequency artifact that occurs when a subject’s PPG signal is recorded [39]. BW reduction is a critical step in the preprocessing of PPG signals because BW makes PPG recordings challenging to interpret. The primary source of BW in the PPG signal is the patient’s movement and respiration [39]. Anything less than 0.5 Hz is a result of baseline wandering. In this study, baseline correction was done by fitting a 4th-degree polynomial to find the trend in the signal and then subtracted the trend to get the baseline-corrected signals, as shown in Fig. 6.

Fig. 5
figure 5

Illustration of PPG signal before and after preprocessing. Filtered signal superimposed on the raw signal

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Fig. 6
figure 6

Correction of the PPG signal’s baseline, a PPG signal with baseline wandering and polynomial trend of fourth degree and b PPG signal after detrending

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Fig. 7
figure 7

Detection and selection of one single PPG cycle from continuous waveform of PPG signal

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3.4 Feature extraction

3.4.1 PPG cycle detection and selection

PPG signal is a continuous waveform, and every individual PPG cycle contains approximately the same information. In this study, one single PPG cycle was used to extract features. Therefore, PPG signals were segmented into a single cycle from 2.1s \(time\_frame\) PPG signals representing a single heartbeat. Normally 2.1s 1 s \(time\_frame\) PPG signals contain two or more cycles. A peak detection algorithm was used to locate the signal peaks. Then each PPG cycle \(C_{PPG}\) was stored in \(S_{PPG}\). Then we extracted all valid PPG cycles. A \(C_{PPG}\) cycle is valid if it contained five important properties. Finally, the best one (\(B_{PPG}\)) was detected automatically by using the peak detection algorithm in Algorithm 1. The detected PPG cycle \(B_{PPG}\) in a \(S_{PPG}\) is depicted in Fig. 7.

Algorithm 1
figure k

PPG cycle detection and selection algorithm

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Table 3 Details of features extracted from each \(S_{PPG}\)
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Fig. 8
figure 8

Features extracted from PPG signal and its derivatives (VPPG and APPG) as well as Fourier Transformed PPG signal

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Finally, by enhancing the analytical technique of Elgendi [35], 46 characteristic features are extracted from the \(B_{PPG}\), as well as its derivatives (\(1^{\text {\tiny st}}\), and \(2^{\text {\tiny nd}}\) order), and Fast Fourier Transformed \(B_{PPG}\) signal. The distributions of these features are as follows: 21 (\(F_1\) to \(F_{21}\)) from the \(B_{PPG}\) signal, 19 (\(F_{22}\) to \(F_{40}\)) from its derivatives (\(1^{\text {\tiny st}}\) and \(2^{\text {\tiny nd}}\) order), and 6 (\(F_{41}\) to \(F_{46}\)) from the Fast Fourier Transformed \(B_{PPG}\) (Table 3). Additionally, age (\(F_{47}\)) and gender (\(F_{48}\)) are provided for each subject as features. Figure 8 depicts the characteristic features of the PPG signal.

3.5 Feature selection

Feature selection refers to selecting the most relevant and non-redundant features to be used in model construction. The fundamental objective of feature selection is to enhance the performance of a predictive model and minimize the computational cost of modeling by selecting the most effective features. Here, four feature selection methods are used: correlation-based feature selection (CFS), ReliefF feature selection (ReliefF), features for classification using minimum redundancy maximum relevance (FSCMRMR), and recursive feature elimination (RFE).

3.5.1 CFS

Correlation is a statistical approach that may be used to assess the presence and strength of relationships between pairs of features. An attribute is acceptable if relevant to the class but not redundant to any of the other relevant attributes [40]. Here, this paper uses the correlation coefficient probability (\(p-value\)) to make good feature subsets containing features highly correlated with the classification but uncorrelated.

Algorithm 2
figure l

Ensemble feature selection technique

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3.5.2 ReliefF

ReliefF is a feature selection algorithm that takes a filtering approach for binary classification with discrete features [41]. This algorithm calculates a feature score for each feature applied to rank and thus chooses the top-scoring features. These scores can be considered as feature weights to handle downstream modeling. The ReliefF algorithm and its derivatives are the only individual evaluation filter algorithms that detect feature dependencies using the concept of nearest neighbours that indirectly capture feature interactions [42].

3.5.3 FSCMRMR

The FSCMRMR algorithm finds an optimal set of mutually and maximally dissimilar features and can show the response variable effectively [15]. The method determines the redundancy and importance of variables based on their mutual information—pairwise mutual information of features and mutual information between a feature and the response. Instead of ranking single variables independently, this algorithm checks a balance between relevance (dependence between the features and the class) and redundancy (dependence among features) [43].

3.5.4 RFE

RFE selects those features in a training datasets which are most relevant in predicting the target by recursively eliminating a small number of features per loop. This in turn results in the elimination of collinearity in the model.

3.5.5 Ensemble feature selection

An ensemble feature selection method based on majority voting is applied to overcome the limitations of conventional feature selection methods [44]. In the beginning, a feature set consisting of 48 features from 218 recorded PPG is fed to an individual feature selection module (FSCMRMR, RLF, CFS, and RFE). Each module results in a set or subset of features for both the SBP and DBP estimations. If any feature selection module selected a feature, one vote was assigned to that feature. Then a voting score was assigned based on how many modules chose a feature. For example, if all modules selected feature \(F_{1}\), its voting score will be four. The procedure of the ensemble feature selection approach is described in Algorithm 2.

Fig. 9
figure 9

The proposed architecture of DNN-based models for SBP and DBP estimation

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Table 4 Status of the hyperparameters used in our proposed DNN-based models
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3.6 Model construction

In this study, a feed-forward deep neural network is adopted to develop the BP estimation model on the basis of extracted features from PPG signals. It is equipped with weights, biases, and activation functions such as a rectified linear unit (ReLU) [45]. Figure 9 illustrates the architecture and training procedure for DNN based models. As demonstrated in Fig. 9, four hidden layers are used, where the first and third hidden layers contain 50 and 150 neurons, respectively. The second hidden layer consists of 100 neurons with a dropout unit of 0.25, while the fourth hidden layer consists of 200 neurons with a dropout unit of 0.50. The dropout method is a more efficient and alternative approach to dealing with DNN overfitting [46]. The output of each hidden layer processing unit can be represented as

$$\begin{aligned} {BP_i} = \sum _i {\omega _i F_i} + \beta \end{aligned}$$
(11)

where \(F_i\), \(\beta \), and \(\omega _i\) denote the input feature vectors, biases, and weights to the neuron, respectively. The hidden layer uses a nonlinear function to transform the input above as

$$\begin{aligned} \varphi _{Re}(BP) = \max (0, BP) \end{aligned}$$
(12)

where \(\varphi _{Re}\) is the ReLU activation function. A linear activation function is applied to the output layer in the final state as

$$\begin{aligned} \varphi _{Li}(BP) = {BP}^\prime \end{aligned}$$
(13)

where \({BP}^\prime \) = \((-\infty , +\infty )\).

Table 5 The selected features from different feature selection algorithms
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As a result, dense layer returns the sum of activation function. The proposed DNN models are trained on 100 epochs with respective batch size and learning rate of 32 and 0.01, respectively. Adam is utilized as the optimizer function to facilitate training processing and update the DNN parameters. Table 4 summarizes the hyperparameters employed in the proposed DNN-based models. These proposed models for BP estimation are trained and tested using all features and selected features.

3.7 Performance measurement parameters

The overall performance of our proposed BP measuring method is evaluated in accordance with the mean difference (ME), standard deviation (STD), mean absolute percentage error (MAPE), mean square error (MSE), root mean square error (RMSE), and the coefficient of determination (\(R^2\)). The formulas are as follows:

$$\begin{aligned} ME = \frac{1}{n} \sum _{n} ({BP}_e - {BP}_a) \end{aligned}$$
(14)
$$\begin{aligned} STD = \sqrt{ \frac{\sum _{n} ({BP}_e - {BP}_a - ME)^2}{n-1}} \end{aligned}$$
(15)
$$\begin{aligned} MAPE = \frac{1}{n} \sum _{n} \left| \frac{{BP}_a - {BP}_e}{{BP}_a} \right| * 100 \end{aligned}$$
(16)
$$\begin{aligned} MSE = \frac{1}{n} \sum _{n} ({BP}_a - {BP}_e)^2 \end{aligned}$$
(17)
$$\begin{aligned} RMSE = \sqrt{MSE} \end{aligned}$$
(18)
$$\begin{aligned} MAE = \frac{1}{n} \sum _{n} \left| {BP}_a - {BP}_e \right| \end{aligned}$$
(19)
$$\begin{aligned} R^2 = 1 - \frac{\sum _{n} ({BP}_a - {BP}_e)^2}{\sum _{n} ({BP}_a - \overline{BP})^2} \end{aligned}$$
(20)

where \(\overline{BP} = \frac{1}{n} \sum _{n} {BP}_a\), and \({BP}_a\) is the reference value while \({BP}_e\) is the estimated value.

4 Result and discussion

4.1 Feature selection

Table 5 demonstrates the outcomes of several features selection techniques. Using feature selection algorithms, features are ranked according to their significance. Both CFS and ReliefF reduced the features from 48 to 16 for SBP, respectively. Similarly, CFS and ReliefF selected only 16 and 17 features, respectively, for DBP. Then, the remaining two FS methods (FSCMRMR and RFE) selected only 5 and 6 features for SBP, whereas 6 and 9 features for DBP, respectively.

Table 6 Voting scores of the corresponding features in the proposed ensemble feature selection approach
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Table 7 Performance comparison using various existing feature selection methods and our proposed ensemble feature selection method along with the DNN models
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Fig. 10
figure 10

Accuracy (\(R^2-\)score) Vs feature selection methods: a SBP and b DBP

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Fig. 11
figure 11

Histograms of estimated errors in DNN-based models: a SBP and b DBP

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Table 6 portraits the voting score of individual features using the ensemble approach (Algorithm 2). In this study, as four different FS methods are applied to the extracted feature set, selecting a feature at least has to have a voting score of two. For both SBP and DBP estimations, it is evident from Table 6 that all the four FS methods voted for features \(F_{47}\). Similarly, features \(F_{28}\), \(F_{25}\), and \(F_{45}\) have a voting score of three for SBP and features \(F_{45}\), \(F_{25}\), \(F_{14}\), \(F_{3}\), and \(F_{41}\) for DBP, respectively. The rest of the features in Table 6 are voted by the two FS methods for both SBP and DBP.

4.2 Robustness performance of models

We used DNN-based models to estimate the SBP and DBP using all features and selected features. A 10-fold cross-validation method was used to divide the data into training and testing sets. It is also noted that each recorded signal of the PPG-BP database has its unique ID. Our study used it to prevent overlapping the subjects of the training set and the testing set.

In the beginning, the proposed DNN-based models are trained and validated using all features for BP value estimation. The DNN models are validated using a 10-fold cross-validation approach, where each fold contains reference and estimated BP values. The mean performances of the models are then calculated following that. Table 7 summarizes the overall performance of the proposed ensemble feature selection method and existing feature selection methods along with our proposed DNN-based models. The estimated accuracies of DNN models using all features are \(R^2 = 0.867\) and MAE = 3.631 mmHg for SBP, 0.805 and 2.387 mmHg for DBP, respectively.

Features selection is crucial to minimize the probability of models getting overfit. Due to this, four feature selection algorithms existing in the literature (CFS, ReleifF, FSCMRMR, and RFE) are used individually for selecting relevant feature subsets. Finally, the selected features from the individual FS method are fed to the DNN models. Among these four FS algorithms, CFS along with the DNN model provided better results of \(R^2 = 0.952\) and MAE = 2.804 mmHg for SBP and ReliefF with \(R^2 = 0.936\) and MAE = 1.796 mmHg for DBP, respectively.

Furthermore, the proposed ensemble feature selection technique is applied to select the best optimal feature set that provided best results when combining with DNN models for the estimation of BP values. According to obtained result in Table 7, this approach provides the highest estimated accuracy of \(R^2 = 0.962\) and MAE = 2.480 mmHg for SBP and 0.955 and 1.499 mmHg for DBP, respectively. Figure 10 shows the accuracy (\(R^2-\)score) respective to various feature selection techniques along with the number of selected features for SBP and DBP, where our proposed ensemble feature selection technique performs better than others.

Figure 11 demonstrates a histogram of estimated errors for BP values. It is evident from both the histograms that the error values for BP estimation are distributed normally around zero. The elemental cause beneath the greater appearance of the estimated error of SBP compared to those of the DBP ones is the dispersion of SBP target values being nearly twice as large as the dispersion of DBP target values.

Figure 12a and c presents a correlation-based comparison of the estimated values with the reference BP values. Furthermore, the Bland–Altman plot is depicted in Fig. 12b and d for evaluating the distance of the estimated value from the reference one. Bland-Altman defines the agreement between the reference value and the estimated value by establishing limits of agreement. It can be concluded from the plots that a higher percentage of estimated values are within the limits of agreement (\(md \pm 1.96*sd\)). The limits of agreement for SBP with hybrid selected features at a 95% confidence interval were {\(-7.87\) mmHg and 6.98 mmHg} and for DBP were {\(-4.88\) mmHg and 4.68 mmHg}. However, samples having extremely high or low BP values are not approximated as accurate as other samples. The main reason of this issue is the presence of fewer subjects with extremely high or low BP within the training set, which restricts the model performance in anticipating continuous BP values.

Fig. 12
figure 12

Correlation and agreement (Bland-Altman) plots of SBP and DBP with reference values at testing stage for DNN model based on hybrid feature selection: a relationship (SBP), b agreement (SBP), c relationship (DBP), and d agreement (DBP)

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Table 8 Comparison of this paper results with AAMI
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Table 9 Comparison of this paper results with BHS
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4.3 Evaluation using the AAMI standard

A comparison between the results of BP estimation using our proposed method and the Advancement of Medical Instrumentation (AAMI) criterion is depicted in Table 8. According to the specification of the AAMI, the mean and standard deviation must not be greater than 5 mmHg and 8 mmHg, respectively, for BP measuring devices. In addition to this criteria, this protocol directs that the number of participants should be at least 85 to ensure the equipment or method’s accuracy. Table 8 shows that our proposed method has mean values that are significantly less than the maximum allowable mean value. In terms of the STD criterion, both SBP and DBP have STD values within the 8 mmHg standard margin.

Table 10 Comparison of our proposed method with several existing methods that only used PPG signal
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4.4 Evaluation using the BHS standard

An illustration for the evaluation of our proposed method according to the British Hypertension Society (BHS) grading criteria is shown in Table 9. BHS grades the BP monitoring devices according to their percentage of cumulative errors underneath three different threshold values, i.e., 5, 10, and 15 mmHg [48]. In accordance with the BHS standard, the performance of our method is persistent, with grade A for both SBP and DBP estimations.

4.5 Comparison with other works

Table 10 presents the comparative analysis of the proposed methodology with the contemporary works to validate the effectiveness of our proposed methodology. From the comparison, it can be seen that our proposed method achieved an average \(MAE \pm STD\) of \( 2.48 \pm 4.105\) mmHg for SBP and \( 1.49 \pm 2.194\) mmHg for DBP estimation which are better compared to the existing methods. It is clear from these results that our proposed methodology can be used in real-time healthcare applications.

Table 10 summarizes previous studies that have estimated the BP using only the PPG signal but have assessed their methodologies using a variety of datasets. Since these research works used different datasets and/or a small number of patients than the proposed approach, it is difficult to make a precise comparison for BP estimation. Furthermore, PPG-BP is a new dataset, and only a few studies have been conducted utilizing this dataset so far. The studies by [15, 22] used the PPG-BG dataset, whereas our proposed technique performed better than these studies.

5 Conclusion

In this paper, we proposed a BP monitoring approach by combining ensemble feature selection technique with deep neural network. Primarily, the proposed methodology consists of signal acquisition, signal filtration, baseline correction, and feature extraction. An ensemble feature selection technique is applied to obtain the most promising feature set based on major voting by four feature selection algorithms. Then, DNN based models are developed, and a 10-fold cross-validation method is applied to validate the models. The combination of the ensemble feature selection method and DNN models provides the best accuracy for estimating continuous blood pressure. The accuracy of our proposed BP estimation method is validated using the AAMI and BHS standards. According to the BHS, our proposed method has grade A for both SBP and DBP estimations. The findings reveal that this approach to BP estimation could be applicable for clinical applications. In the future, we plan to extend our work by including the other physiological parameters such as blood component levels and oxygen saturation (SpO2) as well as computing the whole process automatically in cloud server and sending the result to the smartphone user.